Subharmonic Functions Outside a Compact Set in R n

1982 ◽  
Vol 84 (1) ◽  
pp. 52 ◽  
Author(s):  
Victor Anandam
Keyword(s):  
Compact Set ◽  
Subharmonic Functions

scholarly journals Radon-Nikodym Densities between Harmonic Measures on the Ideal Boundary of an Open Riemann Surface

1966 ◽  
Vol 27 (1) ◽  
pp. 71-76
Author(s):  
Mitsuru Nakai
Keyword(s):  
Riemann Surface ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Dense Subspace ◽  
Compact Set ◽  
Ideal Boundary ◽  
Subharmonic Functions ◽  
Open Riemann Surface ◽  
Harmonic Measures ◽  
The Ideal

Resolutive compactification and harmonic measures. Let R be an open Riemann surface. A compact Hausdorff space R* containing R as its dense subspace is called a compactification of R and the compact set Δ = R* -R is called an ideal boundary of R. Hereafter we always assume that R does not belong to the class OG. Given a real-valued function f on Δ, we denote by the totality of lower bounded superharmonic (resp. upper bounded subharmonic) functions sonis satisfying

scholarly journals The Dirichlet problem for $m$-subharmonic functions on compact sets

2020 ◽  
Vol 126 (3) ◽  
pp. 497-512
Author(s):  
Per Åhag ◽  
Rafał Czyż ◽  
Lisa Hed
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Functions ◽  
Compact Set ◽  
Compact Sets ◽  
Subharmonic Functions

We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous $m$-subharmonic functions defined on a compact set, and then within the class of $m$-harmonic functions.

On the non-admissible subharmonic functions

1978 ◽  
Vol 64 (1) ◽  
pp. 15-20
Author(s):  
Victor Anandam
Keyword(s):  
Subharmonic Functions

scholarly journals A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 82
Author(s):  
Alejandro Rincón ◽  
Gloria M. Restrepo ◽  
Fredy E. Hoyos
Keyword(s):  
Lyapunov Functions ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Second Order ◽  
Control Law ◽  
Compact Set ◽  
State Variables ◽  
Robust Observer

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

scholarly journals Application of Psychometric Approach for ASD Evaluation in Russian 3–4-Year-Olds

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1608
Author(s):  
Andrey Nasledov ◽  
Sergey Miroshnikov ◽  
Liubov Tkacheva ◽  
Kirill Miroshnik ◽  
Meriam Uld Semeta
Keyword(s):  
Autistic Spectrum Disorder ◽  
Online Survey ◽  
Total Sample ◽  
Compact Set ◽  
Healthy Controls ◽  
Screening System ◽  
Children With Asd ◽  
Discriminant Analyses ◽  
Biological Problem ◽  
Choice Tasks

Background: Autistic spectrum disorder (ASD) is a significant socio-biological problem due to its wide prevalence and negative outcomes. In the current study, we aimed to develop an autism scale for early and accurate differentiation of 3- to 4-year-olds at risk for ASD since there is no systematic monitoring of young children in Russia yet. Methods: The total sample (N = 324) included 116 children with ASD, 131 children without ASD (healthy controls), and 77 children with developmental delay (DD). An online survey of specialists working with children was conducted based on a specially designed autism questionnaire consisting of 85 multiple-choice tasks distributed across 12 domains. Initially, each child was assessed by 434 items using a dichotomous scale (0 = no, 1 = yes). Factor and discriminant analyses were performed to identify a compact set of subscales that most accurately and with sufficient reliability predicted whether a child belongs to the ASD group. Results: As a result, four subscales were obtained: Sensorics, Emotions, Hyperactivity, and Communication. The high discriminability of the subscales in distinguishing the ASD group from the non-ASD group was revealed (accuracy 85.5–87.0%). Overall, the obtained subscales meet psychometric requirements and allow for creating an online screening system for wide application.

scholarly journals Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

4OR ◽  
2020 ◽  
Author(s):  
Michele Conforti ◽  
Marianna De Santis ◽  
Marco Di Summa ◽  
Francesco Rinaldi
Keyword(s):  
Integer Point ◽  
Cutting Plane ◽  
Integer Program ◽  
Compact Set ◽  
Cutting Plane Method ◽  
Integer Points ◽  
Gomory Cuts ◽  
The Family ◽  
Split Cuts ◽  
Number Of Iterations

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x ∈ S ∩ Z n } , where $$S\subset \mathbb {R}^n$$ S ⊂ R n is a compact set and $$c\in \mathbb {Z}^n$$ c ∈ Z n . We analyze the number of iterations of our algorithm.

scholarly journals A maximum principle

1979 ◽  
Vol 28 (1) ◽  
pp. 23-26
Author(s):  
Kung-Fu Ng
Keyword(s):  
Maximum Principle ◽  
Extreme Point ◽  
Convex Space ◽  
Maximal Element ◽  
Locally Convex Space ◽  
Compact Set ◽  
Natural Manner ◽  
Upper Semicontinuous ◽  
Nonempty Compact ◽  
Locally Convex

AbstractLet K be a nonempty compact set in a Hausdorff locally convex space, and F a nonempty family of upper semicontinuous convex-like functions from K into [–∞, ∞). K is partially ordered by F in a natural manner. It is shown among other things that each isotone, upper semicontinuous and convex-like function g: K → [ – ∞, ∞) attains its K-maximum at some extreme point of K which is also a maximal element of K.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 46 A 40.

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